I’m studying and need help with a Algebra question to help me learn.
1. Consider the line passing through (9,150) and with slope−23
(a) Define the input atsand the output atr. What isr(9)?(
b) Create a table fitting this data that has 5 different points. Do not use an equation to find thesepoints.
(c) Supposesis the time in seconds andris the radius in centimeters. As the seconds get larger is theradius increasing or decreasing?
(d) Interpret 2 of the points in the table.
(e) Interpret the slope.
(f) Give an equation in point-slope form for this line using function notation.(g) Use the order of operations and simplifying to write the equation in the previous part into slope-intercept form. Use function notation.
(h) When will the radius be 0 cm?
(i) What was the radius at the start (0 seconds)?
(j) Suppose this equation just gives estimates. At 9 seconds the radius was actually 160 cm. How faroff was the estimate?
(k) Find the residual for 12 seconds if the actual radius was 140 cm.
(l) Is this linear proportional or linear non-proportional? How do you know?
2. 40 cupcakes cost $50 and 30 cupcakes cost $40. There is a set cost per cupcake and a fixed cost for delivery.
(a) Write this data in a table. Define your variables and do not usexandy.(b) What is the slope? Interpret the slope.
(c) Give the equation of the line passing through these points in point-slope form. Use function notation.
(d) Give the equation of the line in slope-intercept form by simplifying the above equation step-by-step.(
e) What is the vertical intercept of the line that passes through these points? Interpret this intercept.
(f) What is the delivery cost?
(g) What is the cost per cupcake?
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